Saçu İbrahim Ethem
Clinical Engineering Research and Implementation Center (ERKAM), Erciyes University, 38030 Kayseri, Turkey.
Cogn Neurodyn. 2024 Feb;18(1):247-263. doi: 10.1007/s11571-023-09933-3. Epub 2023 Feb 7.
Dynamic analysis, electrical coupling and synchronization control of the conformable FitzHugh-Nagumo neuronal models have been presented in this work. Firstly, equations of the Adomian-Decomposition-Method and conformable neuron model have been introduced. The Adomian-Decomposition-Method has been employed for the numerical simulation analysis, since it converges fast and provides serial solutions. Fractional order and external current stimulus have been considered as bifurcation parameters and their effects on neuron model dynamics have been examined in detail. Then, the electrical coupling of the two conformable neuronal models without any controller has been revealed and the significance of the coupling strength parameter has been evaluated. To eliminate impact of the coupling strength parameter on synchronization status of neurons, Lyapunov control method has been employed for synchronization control. In the last step, the numerical simulation studies have been experimentally verified using the Texas Instrument Delfino digital signal processor board. Numerical simulation results together with experimental validation have showed that the types of dynamics of the related neuron model are not affected from the change of the fractional order of conformable derivative, but the frequency of the dynamic response of the neuronal model is changed from the alteration of the fractional order. The frequency of response of the neuron model increases with decreasing values of the fractional order. On the other hand, if there is no synchronization control method, the coupled neuron models exhibit response ranging from synchronous to asynchronous depending on the sign and value of the coupling parameter. Additionally, decreasing values of the fractional order may allow the coupled neurons to enter the synchronous state more quickly due to increasing frequency of response of the neuronal model. Finally, the coupled neuron models could exhibit synchronous behavior, that is determined by calculating the standard deviation results, regardless of the value of the coupling parameter by using the Lyapunov control method.
本文对适形FitzHugh-Nagumo神经元模型进行了动力学分析、电耦合及同步控制。首先，介绍了阿多米安分解法和适形神经元模型的方程。由于阿多米安分解法收敛速度快且能提供级数解，因此被用于数值模拟分析。分数阶和外部电流刺激被视为分岔参数，并详细研究了它们对神经元模型动力学的影响。然后，揭示了两个无控制器的适形神经元模型的电耦合，并评估了耦合强度参数的意义。为消除耦合强度参数对神经元同步状态的影响，采用李雅普诺夫控制方法进行同步控制。在最后一步，使用德州仪器Delfino数字信号处理器板对数值模拟研究进行了实验验证。数值模拟结果与实验验证表明，相关神经元模型的动力学类型不受适形导数分数阶变化的影响，但神经元模型动态响应的频率会因分数阶的改变而变化。神经元模型的响应频率随分数阶值的减小而增加。另一方面，如果没有同步控制方法，耦合神经元模型根据耦合参数的符号和值表现出从同步到异步的响应。此外，分数阶值的减小可能会使耦合神经元由于神经元模型响应频率的增加而更快地进入同步状态。最后，通过计算标准差结果可知，使用李雅普诺夫控制方法时，耦合神经元模型能够表现出同步行为，而与耦合参数的值无关。
